The numerical simulation of temporally accelerated flow subjected to Favorable and Adverse pressure Gradients (FPG & APG) is represented. Two accelerations are considered and imposed on fully turbulent flow over a flat plate. The γ-SST model is implemented to define the boundary layer development, turbulence structures, and the wall functions responses to the external accelerated flow. The obtained results illustrate that the FPG condition accompanied by temporal acceleration can severely damp the fluctuations. So, an almost-laminar boundary layer develops near the wall, followed by a retransition to the higher turbulent state. However, the APG condition provides higher turbulence diffusion in a temporal accelerated flow. It makes the flow more orderly and more stable, although a re-laminarization is observable in this region excessively. Moreover, the applied condition disturbs the Reynolds stress correlation and generates semi-elliptic eddies because acceleration affects wall-normal fluctuations more severely than the streamwise ones. Also, a new represented acceleration parameter for this condition is compared with the acceleration parameter in spatially accelerated flow.